E. T. Jaynes' subjectivism vs measurement of distributions

Question

In his paper, E. T. Jaynes argues that entropy is a measure of our ignorance about a system. As such, the probability distribution of states $\{p_k\}$ has to be chosen in the most unbiased way, thus maximizing the entropy constrained to all the available information. This is a subjectivist point of view because treats probabilities as description of our ignorance, rather than as an intrinsic property of the system. He also claims that the reason statistical mechanics works is that the distributions are sharply peaked and, as long as the peak is at the correct position, its shape is not that relevant.

With the development of computers and experiments, however, now we are able to simulate distributions of states in a system or measure actual equilibrium fluctuations at a high resolution (with optical tweezers, for example). Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states. Measurements show that these are indeed the distributions that maximize entropy (at constant temperature, for instance, it's the Boltzmann distribution). How would a subjectivist argue then that the probability of states are due to our lack of information about the system? If I can measure those distributions, they look very objective to me.

Answer 1

Going beyond macroscopic quantities, thus, we can simulate/measure actual probability distributions of states.

This is a misunderstanding. One never measures probability, the verb does not apply to the noun. In such simulations/calculations one may record some numbers, such as number of times the system was found in some region of phase space (or number of times system assumed some definite microstate). Such numbers can be divided by total number of observations or total number of time points, but this only gives frequency of occurences in that simulation, an artefact that depends on initial condition that may not repeat itself with different initial condition. It can serve as estimate of the probability, but itself is not the probability, which is supposed to abstract from details such as the initial condition. Jaynes provides a coherent way to think about the probability and a way to find probabilities in a number of cases of interest in statistical physics, using the maximum information entropy principle. Of course, one should test, if possible, usefulness of so determined probabilities, for example through computer simulations of concrete cases.

Answer 2

On the basis of the present classification of probability interpretations, I would not classify Jaynes' approach as subjectivism, even if Jaynes presented his approach in this way. Certainly it is a Bayesian point of view, but not a subjectivist one. Both Bayesian and subjectivism look at probabilities as a measurement of the state of knowledge. But such a measurement, for a subjectivist, is directly related to the quantification of a personal belief, while objective Bayesian approach tries to build "objective" priors, for example using maxent method, where the role of the objective knowledge about the system is quite clear.

In a Bayesian approach to probability (and then to Statistical Mechanics) the success of the theory should be seen as a confirmation about the choice of the priors. Therefore, there is no conflict between the fact that one can check the consistence between measured frequencies and probabilities and the knowledge about the system which has been used to establish the priors.